Valve are continuing their polishing effort to make the Steam Client work better, with a load of work from the recent Beta releases now out for everyone.

This Steam Client update includes an updated version of their embedded Chromium build, it adds in a Big Picture Mode library filter for local multiplayer games, multiple changes to Steam Input including a new "Controller Connected" notification (which can be turned off), the ability to blacklist individual DirectInput and Xinput devices in the controller settings menu, improvements to in-home streaming, Vulkan pipeline dumping and collection if Shader Pre-Caching is enabled and more.

As I understand it, the Vulkan part above is so the shader cache for a Vulkan game can be uploaded to Steam and shared, so we would hopefully see less stuttering which would be a big improvement.

For Linux specifically, these issues were fixed and improved:

Fixed more instances of 0-byte downloads and missing Proton or data files for Steam Play titles

Added Steam Play configuration settings in Big Picture Mode

Fixed an issue where the mouse cursor would be invisible in the Steam Overlay when playing games through Steam Play

Fixed an issue where the Steam Client wouldn’t automatically update or download Proton before launching games through Steam Play

Fixed additional cursor and mouse grabbing issues with the overlay on Steam Play games.

"What would you like to see improved next in the Steam Client?"
updates to the oficial list of games white listed by valve.
it may seem something small, but the protonDB database isnt realiable, some people rate the game as platinum without knowing about all the features that the game have in order to be able to test it and make sure everything is working, so some "platinum" or "gold" ratings are false positives.
example: guilty gear dont have any videos on proton (neither the intro, nor the extras nor anything else that the game may have, looks like the issue is that the codec for then is WMV, but that is an issue that valve can easily fix asking devs to convert the videos and distribute alongside the game (or convert then selfs asking permission to redistribute it)
another issue is features like hair works that may not work on linux, but the game be rated platinum regardless.

elmapul"What would you like to see improved next in the Steam Client?"
updates to the oficial list of games white listed by valve.
it may seem something small, but the protonDB database isnt realiable, some people rate the game as platinum without knowing about all the features that the game have in order to be able to test it and make sure everything is working, so some "platinum" or "gold" ratings are false positives.
example: guilty gear dont have any videos on proton (neither the intro, nor the extras nor anything else that the game may have, looks like the issue is that the codec for then is WMV, but that is an issue that valve can easily fix asking devs to convert the videos and distribute alongside the game (or convert then selfs asking permission to redistribute it)
another issue is features like hair works that may not work on linux, but the game be rated platinum regardless.

Related to this request of yours, I feel like mentioning that I have had a couple of ProtonDB and Steam purchase experiences recently that might help you (and others reading).

I wanted to purchase the Windows-only game "UnExplored" which was on sale on Steam a few weeks ago. My reasoning was - It is listed as Bronze status on ProtonDB - and I can purchase it, test it for 2 hours, and if it fails to run with Proton/Steam Play then I can request a refund. Well, the game didn't run for me with Proton so I made a refund request to Steam, got the refund, the game was removed from my library - All good. It might be possible to get UnExplored working, using tweaks, but I didn't discover one during my short test. (I reported my BORKED failure back onto ProtonDB list, and note that some other people have got it working.) My advice: Get the game, and take advantage of the grace period, and get refunded if it doesn't work.

Proton/Steam Play is a work in progress and as much as it is getting better and better, I'm aware that there is potential for some games to work and others to fail and there might be tweaks needed for some games. That is the nature of it. I'm happy for progress to be going ahead, and it would be good if the Supported Games list was swelled, but give them a chance - This is quite new, experimental work going on here.

Back to my latest (yesterday's 4.2-3 release) experiences with Proton and ProtonDB. Hurray! Of my 16 installed Proton games, currently only one game isn't working (The game which is failing is "Antihero".)

I have at last got Fallout 3 GOTY and Elder Scrolls Skyrim SE working with full NPC audio and all working as expected, BUT I needed to apply relatively simple "Set Launch Options" into the game's Properties dialogue for the games to run correctly.

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